Standard deviation of weighted average

Example: Four series of measurements are made and arithmetic means calculated
=1,7982 V, = 1,8022 V, =1,7984 V and =1,7994 V with standard deviation s1=0,0161 V, s2=0,0164 V, s3=0,0116 V and s4=0,0112 V. The best estimates of measurand and uncertainty caused by random effects should be estimated.

If we take that constant from equation for weight factor we get:
w1= 1,04
w2= 1,00
w3= 2,00
w4= 2,14

The best estimate of measurement result is weighted average:

Standard deviation of weighted average is calculated as:

Based on series of four measurement results the most qualitative measurement result is
(1,7993 0,0066) V.

:: EXAMPLES ::

Proper expression of measurement result on M level.
Proper expression of measurement result on L level.
Correct expression of measurement result.
Absolute, relative and percentage errors.
Determination of resistance measurement uncertainty.
Expression of measurement result represented with expanded uncertainty.
Corrected measurement result.
Standard deviation of arithmetic mean.
Measurement with analog instrument.
Measurement with digital instrument.
Estimation of uncertainty from worst-case limits of error
Combined measurement uncertainty
U-I method for measuring small resistance
Measuring resistance with digital ohmmeter